[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.j160465

ON SPLIT LEIBNIZ TRIPLE SYSTEMS

Cao, Yan (School of Mathematics and Statistics Northeast Normal University)
Chen, Liangyun (School of Mathematics and Statistics Northeast Normal University)

Publication Information

Journal of the Korean Mathematical Society / v.54, no.4, 2017 , pp. 1265-1279 More about this Journal

Abstract

In order to study the structure of arbitrary split Leibniz triple systems, we introduce the class of split Leibniz triple systems as the natural extension of the class of split Lie triple systems and split Leibniz algebras. By developing techniques of connections of roots for this kind of triple systems, we show that any of such Leibniz triple systems T with a symmetric root system is of the form $T=U+{\sum}_{[j]{\in}{\Lambda}^1/{\sim}}I_{[j]}$ with U a subspace of $T_0$ and any $I_{[j]}$ a well described ideal of T, satisfying $\{I_{[j]},T,I_{[k]}\}=\{I_{[j]},I_{[k]},T\}=\{T,I_{[j]},I_{[k]}\}=0 \text{ if }[j]{\neq}[k]$ .

Keywords

split Leibniz triple system; Lie triple system; Leibniz algebra; root system; root space;

Citations & Related Records

Reference

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